Question

Point charges of $3\times 10^{-9}C$ situated at each of three comers of a square whose side is 15 cm. The magnitude and direction of A electric field at the vacant corner of the square is

• A. 2296 y/m along the diagonal
• B. 9622 V/m along the diagonal
• C. 22.0 V/m along the diagonal
• D. zero

Answer 1

Answer: (A)

Effective electric field will be $\sqrt{2}{E}_1+E_2$ along the diagonal.
$\Rightarrow E=\frac{k{q}_1}{{\left(15\times 10^{-2}\right)}^2}\sqrt{2}+\frac{k{q}_1}{{\left(\sqrt{2}\times 15\times 10^{-2}\right)}^2}$
$=\frac{9\times 10^9\times 3\times 10^{-9}\times \sqrt{2}}{225\times 10^{-4}}+\frac{9\times 10^{-9}\times 3\times 10^{-9}}{2\times 225\times 10^{-4}}$
$=\frac{38.1}{225\times 10^{-4}}+\frac{13.5}{225\times 10^{-4}}$
$=\frac{51.6}{225\times 10^{-4}}$
$E=2293.33V/m$
$=2294V/m$